As we know, escape velocity,

${V_e} = \sqrt {{{2GM} \over R}} = \sqrt {{{2G} \over R}.\left( {{4 \over 3}\pi {R^3}\rho } \right)} \propto R\sqrt \rho$

$\therefore$ ${{{V_e}} \over {{V_p}}} = {{{R_e}} \over {{R_p}}}\sqrt {{{{\rho _e}} \over {{\rho _p}}}}$

$\Rightarrow {{{V_e}} \over {{V_p}}} = {{{R_e}} \over {2{R_e}}}\sqrt {{{{\rho _e}} \over {2{\rho _e}}}}$

$\therefore$ Ration ${{{V_e}} \over {{V_p}}} = 1:2\sqrt 2$